Standing water in gas heater pan...dangerous to wait?

We moved into a rental house with a 13 year old gas water heater. There's about 2 inches of moldy water in the bottom pan. The heater is lit and providing hot water throughout the house fine. There doesn't seem to be any active leaks, as the water isn't increasing...just standing and moldy. Landlord is installing a new one next week. Is there any danger in letting the current one run until then, standing water and all? I'm getting ready to go out and buy one tomorrow instead of waiting but wondering if I'm worried for no reason.

why isnt the pan draining? is a drain hooked up?

just dip the water out. cut the top off of a plastic coke bottle

throw a 1/4 cup of bleach in the water then dip it into a bucket, pour it outside